Rksuite: a Suite of Explicit Runge-kutta Codes

DENSERKS: A suite of Fortran sensitivity solvers using continuous, explicit Runge-Kutta schemes

2-stage explicit total variation diminishing preserving Runge-Kutta methods

In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious o...

PII : S 0898 - 1221 ( 96 ) 00141 . 1 An Efficient Runge - Kutta ( 4 , 5 ) Pair

-A pair of explicit Runge-Kutta formulas of orders 4 and 5 is derived. It is significantly more efficient than the Fehlberg and Dormand-Prince pairs, and by standard measures it is of at least as high quality. There are two independent estimates of the local error. The local error of the interpolant is, to leading order, a problem-independent function of the local error at the end of the step. ...

Nonstandard explicit third-order Runge-Kutta method with positivity property

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

Development of Openfoam Solvers for Incompressible Navier–stokes Equations Based on High-order Runge–kutta Schemes

Nowadays open-source CFD codes provide suitable environments for implementation and testing low-dissipative algorithms typically used for turbulence simulation. Moreover these codes produce a reliable tool to test high-fidelity numerics on unstructured grids, which are particularly appealing for industrial applications. Therefore in this work we have developed several solvers for incompressible...